lec0201 - CS 173: Discrete Mathematical Structures Cinda...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 173: Discrete Mathematical Structures Cinda Heeren heeren@cs.uiuc.edu Rm 2213 Siebel Center Office Hours: W 9:30-11:30a
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cs173 - Spring 2004 CS 173 Announcements Homework 2…  Homework 3 available.  Due 02/05, 8a. Midterm 1:  2/23/06, 7-9p, location TBA. Let’s try the remotes… For breakfast I ate: a) cereal b) eggs c) brew d) donuts
Background image of page 2
Cs173 - Spring 2004 CS 173 Set Theory - Definitions and notation A set is an unordered collection of elements. Some examples: {1, 2, 3} is the set containing “1” and “2” and “3.” {1, 1, 2, 3, 3} = {1, 2, 3} since repetition is irrelevant. {1, 2, 3} = {3, 2, 1} since sets are unordered. {1, 2, 3, …} is a way we denote an infinite set (in this case, the natural  numbers).  = {} is the empty set, or the set containing no elements. Note:     {
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cs173 - Spring 2004 CS 173 Set Theory - Definitions and notation  S means “x is an element of set S.”  S means “x is not an element of set S.”  B means “A is a subset of B.” Venn Diagram or, “B contains A.” or, “every element of A is also in B.” or, 2200 x ((x A) (x B)). A B
Background image of page 4
Cs173 - Spring 2004 CS 173 Set Theory - Definitions and notation  B means “A is a subset of B.”  B means “A is a superset of B.” A = B if and only if A and B have exactly the same elements. iff, A   B and B   A iff, A   B and A   B  iff,  2200 x ((x   A)   (x   B)). So to show equality of sets A and B, show:  B  A
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cs173 - Spring 2004 CS 173 Set Theory - Definitions and notation  B means “A is a proper subset of B.”  B, and A   B. 2200 x ((x   A)   (x   B))    ¬2200 x ((x   B)   (x   A)) 2200 x ((x   A)   (x   B))    5 ¬ ( ¬ (x   B) v (x   A)) 2200 x ((x   A)   (x   B))    5 x ((x   B)    ¬ (x   A)) 2200 x ((x   A)   (x   B))    5 x ((x   B)   (x   A)) A B
Background image of page 6
Cs173 - Spring 2004 CS 173 Set Theory - Definitions and notation Quick examples: {1,2,3}   {1,2,3,4,5} {1,2,3}   {1,2,3,4,5}  Is     {1,2,3}? Yes!  2200 x (x     (x   {1,2,3}) holds,  because (x    ) is false. Is     {1,2,3}? No!  Is     { ,1,2,3}? Yes!  Is     { ,1,2,3}? Yes!  Vacuously
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cs173 - Spring 2004 CS 173 Set Theory - Definitions and notation Quiz time: Is {x}   {x}?
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 33

lec0201 - CS 173: Discrete Mathematical Structures Cinda...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online